Side Splitter/Angle Bisector Flashcard

Front

What is the Side Splitter Theorem?

Back

The Side Splitter Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

Define an angle bisector.

Back

An angle bisector is a line or ray that divides an angle into two equal parts.

Front

How do you find the length of a segment using the Side Splitter Theorem?

Back

To find the length of a segment using the Side Splitter Theorem, set up a proportion between the segments created by the parallel line and solve for the unknown length.

Front

What is the relationship between the angles formed by an angle bisector?

Back

The angles formed by an angle bisector are equal; each angle measures half of the original angle.

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

The corresponding sides of similar triangles are in proportion.

Front

What is the formula for the Angle Bisector Theorem?

Back

The Angle Bisector Theorem states that if a point D lies on the angle bisector of angle A, then AD/AC = BD/BC.

Front

How can you determine if two triangles are similar using angle bisectors?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar by the Angle-Angle (AA) similarity criterion.

Front

What is the significance of the Side Splitter Theorem in solving problems?

Back

The Side Splitter Theorem helps in finding unknown lengths in triangles and establishing relationships between different segments.

Front

If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem (3^2 + 4^2 = 5^2).

Front

What is the first step in solving for x in a triangle problem involving angle bisectors?

Back

Identify the angles and segments involved, and set up the appropriate proportion or equation.